A diesel engine, in which an engine exhaust passage is branched to a pair of exhaust branch passages for purifying NO.sub.x, containing a switching valve which is disposed at the branching portion of the exhaust branch passages to alternately guide the exhaust gas to one of the exhaust branch passages by a switching function of the switching valve, and a catalyst which can oxidize and absorb the NO.sub.x and which is disposed in each of the exhaust branch passages, is well known (refer to Japanese Unexamined Patent Publication No. 62-106826). In this diesel engine, NO.sub.x in the exhaust gas introduced into one exhaust branch passage is oxidized and absorbed by the catalyst disposed in that exhaust branch passage. During this time, the inflow of the exhaust gas to the other exhaust branch passage is stopped and, at the same time, a gaseous reducing agent is fed into this exhaust branch passage. The NO.sub.x accumulated in the catalyst disposed in this exhaust branch passage is reduced by this reducing agent. Subsequently, after a short time, the introduction of the exhaust gas to the exhaust branch passage to which the exhaust gas had been introduced heretofore is stopped by the switching function of the switching valve, and the introduction of the exhaust gas to the exhaust branch passage to which the introduction of the exhaust gas had been stopped heretofore is started again.
In such a catalyst, to properly oxidize and absorb NO.sub.x, it is necessary to increase the amount of alkali metals, alkali-earth metals or rare-earth metals to more than a given amount. However, if the amount of alkali metals, alkali-earth metals or rare-earth metals is increased, the alkalinity is increased and, as a result, the reducing force of the catalyst is weakened. Accordingly, when NO.sub.x absorbed in the NO.sub.x absorbent should be reduced, NO.sub.x cannot be sufficiently reduced, and thus a problem arises in that a large amount of NO.sub.x is discharged into the outside air without being reduced.